Duckworth–Lewis–Stern method

After the retirement of both Duckworth and Lewis, the Australian statistician Steven Stern became the custodian of the method, which was renamed to its current title in November 2014.

[2][3] In 2014, he refined the model to better fit modern scoring trends, especially in T20 cricket, resulting in the updated Duckworth-Lewis-Stern method.

"[6][7] The D/L method avoids this flaw: in this match, the revised D/L target of 236 would have left South Africa needing four to tie or five to win from the final ball.

If it is a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to: The original D/L model started by assuming that the number of runs that can still be scored (called

This method relies on the assumption that average performance is proportional to the mean, irrespective of the actual score.

[15] To overcome the problem, an upgraded formula was proposed with an additional parameter whose value depends on the Team 1 innings.

The retrospective D/L target from 5 overs was a further reduction to 44, or a par score of 43, and hence Sri Lanka won the match by 14 runs.

At a second rain interval, England, who had scored some quick runs (knowing they needed to get ahead in D/L terms) would correspondingly have won if play had not resumed.

This example does show how crucial (and difficult) the decisions of the umpires can be, in assessing when rain is heavy enough to justify ceasing play.

[23][24] The published table that underpins the D/L method is regularly updated, using source data from more recent matches; this is done on 1 July annually.

This used a single published reference table of total resource percentages remaining for all possible combinations of overs and wickets,[26] and some simple mathematical calculations, and was relatively transparent and straightforward to implement.

However, a flaw in how it handled very high first innings scores (350+) became apparent from the 1999 Cricket World Cup match in Bristol between India and Kenya.

One-day matches were achieving significantly higher scores than in previous decades, affecting the historical relationship between resources and runs.

In 2002 the resource percentages were revised, following an extensive analysis of limited overs matches, and there was a change to the G50 for ODIs.

Lewis was quoted admitting that "Certainly, people have suggested that we need to look very carefully and see whether in fact the numbers in our formula are totally appropriate for the Twenty20 game.

"[33] For the 2015 World Cup, the ICC implemented the Duckworth–Lewis–Stern formula, which included work by the new custodian of the method, Professor Steven Stern, from the Department of Statistics at Queensland University of Technology.

These changes recognised that teams need to start out with a higher scoring rate when chasing high targets rather than keep wickets in hand.

The total resources available to a team are given by:[26] which can alternatively be written as: Each time there's an interruption or a restart after an interruption, the resource remaining percentages at those times (obtained from a reference table for the Standard Edition, or from a computer for the Professional Edition) can be entered into the formula, with the rest left blank.

In fact it would be possible for the two captains to agree a value of G50 before the start of each match, taking account of all relevant factors.

If Hampshire's target had been set by the Average Run Rate method (simply in proportion to the reduction in overs), their par score would have been 231 x 28/30 = 215.6, giving 216 to win or 215 to tie.

Increasing the Netherlands' target score neutralises the injustice done to Australia when they were denied some of the overs to bat they thought they would get.

However, if this is true, this belief was mistaken, in the same way that conserving wickets rather than maximising runs in the final 8 overs of a full 50-over innings would be a mistake.

Therefore, the best batting strategy for Team 1 ahead of a coming interruption is not always the same, but varies with the facts of the match situation to date (runs scored, wickets lost, overs used, and whether there have been interruptions), and also with the opinions about what will happen with each strategy (how many further runs will be scored, further wickets will be lost, and further overs will be used?

This example shows just two possible batting strategies, but in reality there could be a range of others, e.g. 'neutral', 'semi-aggressive', 'super-aggressive', or timewasting to minimise the amount of resource used by slowing the over rate.

There are uses of the D/L method other than finding the current official final target score for the team batting second in a match that has already been reduced by the weather.

Another criticism is that the D/L method does not account for changes in proportion of the innings for which field restrictions are in place compared to a completed match.

[55] More recent efforts have used ball-by-ball ODI databases of actually completed matches to evaluate the accuracy of the method.

[57][58] For example, in a one-day match against England on 20 March 2009, the West Indies coach (John Dyson) called his players in for bad light, believing that his team would win by one run under the D/L method, but not realising that the loss of a wicket with the last ball had altered the Duckworth–Lewis score.

In fact Javagal Srinath, the match referee, confirmed that the West Indies were two runs short of their target, giving the victory to England.

[59] The Duckworth Lewis Method is the name of a pop group, formed by Neil Hannon of The Divine Comedy and Thomas Walsh of Pugwash.